I don't think your split of "taking care of data, getting stuff done, and showing data" actually reflects the intent of MVC. It does reflect how most people use Catalyst though. I would expect an MVC app to have a controller that does nothing but map input to methods in the model. It would know nothing about the application itself, but plenty about the web, i.e. the point of the controller is to separate things that are web-specific about user input from the model. That is all it should do. If you want to run your model from a Tk GUI, you just make a new controller and view that understand Tk.
We do have a bit of a problem at this point, since no other useful name has evolved for the style of development you are talking about. Calling it MVC isn't accurate, but calling it "a templated web app with an O/R mapper" is not succinct enough.